When viewing a message you should be able to select text and then when you hit reply that selected text with the header/from should be the only "new" text in the reply message. Otherwise the entire message should be included in the new reply.
I think you should probably just use vim to trim the message down, however I believe this feature is still going to be needed if you want to copy/extract a long section of text to the system clipboard ala tmux. If the message is longer than a screen, you can't just copy-paste it normally. Probably bind this to V to match vim's visual mode and just make it a line copy rather than on word boundaries.
I think mutt at any point lets you open the email in an editor to do more advanced things, so having another button for that might prove useful, or at least a function that can be hooked.